Related papers: Physics-Informed Neural Operator for Electromagnet…
In this paper, we propose physics-informed neural operators (PINO) that combine training data and physics constraints to learn the solution operator of a given family of parametric Partial Differential Equations (PDE). PINO is the first…
Fourier Neural Operator (FNO) is a powerful and popular operator learning method. However, FNO is mainly used in forward prediction, yet a great many applications rely on solving inverse problems. In this paper, we propose an invertible…
The physics-informed neural operator (PINO) is a machine learning paradigm that has demonstrated promising results for learning solutions to partial differential equations (PDEs). It leverages the Fourier Neural Operator to learn solution…
Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or…
Fractional diffusion equations have been an effective tool for modeling anomalous diffusion in complicated systems. However, traditional numerical methods require expensive computation cost and storage resources because of the memory effect…
Learning accurate and stable time-advancement operators for nonlinear partial differential equations (PDEs) remains challenging, particularly for chaotic, stiff, and long-horizon dynamical systems. While neural operator methods such as the…
Predicting the microstructural and morphological evolution of materials through phase-field modelling is computationally intensive, particularly for high-throughput parametric studies. While neural operators such as the Fourier neural…
Physics-informed neural networks (PINNs) and neural operators (NOs) for solving the problem of diffraction of Extreme Ultraviolet (EUV) electromagnetic waves from contemporary lithography masks are presented. A novel hybrid Waveguide Neural…
Physics-informed neural operators have emerged as a powerful paradigm for solving parametric partial differential equations (PDEs), particularly in the aerospace field, enabling the learning of solution operators that generalize across…
Learning maps between function spaces with a strong inductive bias is a central challenge in soft computing, especially when training data are scarce and standard deep architectures overfit. We introduce a \emph{neural integral operator}…
Accurate real-time prediction of phase-resolved ocean wave fields remains a critical yet largely unsolved problem, primarily due to the absence of practical data assimilation methods for reconstructing initial conditions from sparse or…
We propose an extended Fourier neural operator (FNO) architecture for learning state and linear quadratic additive optimal control of systems governed by partial differential equations. Using the Ehrenpreis-Palamodov fundamental principle,…
Physics-Informed Neural Operators provide efficient, high-fidelity simulations for systems governed by partial differential equations (PDEs). However, most existing studies focus only on multi-scale, multi-physics systems within a single…
The predictive accuracy of operator learning frameworks depends on the quality and quantity of available training data (input-output function pairs), often requiring substantial amounts of high-fidelity data, which can be challenging to…
As artificial intelligence emerges as a transformative enabler for fusion energy commercialization, fast and accurate solvers become increasingly critical. In magnetic confinement nuclear fusion, rapid and accurate solution of the…
Fourier Neural Operators (FNO) offer a principled approach to solving challenging partial differential equations (PDE) such as turbulent flows. At the core of FNO is a spectral layer that leverages a discretization-convergent representation…
Initial boundary value problems arise commonly in applications with engineering and natural systems governed by nonlinear partial differential equations (PDEs). Operator learning is an emerging field for solving these equations by using a…
Modelling complex multiphysics systems governed by nonlinear and strongly coupled partial differential equations (PDEs) is a cornerstone in computational science and engineering. However, it remains a formidable challenge for traditional…
In this paper we employ the emerging paradigm of physics-informed neural networks (PINNs) for the solution of representative inverse scattering problems in photonic metamaterials and nano-optics technologies. In particular, we successfully…
We present a neural operator framework for solving inverse scattering problems. A neural operator produces a preliminary indicator function for the scatterer, which, after appropriate rescaling, is used as a regularization parameter within…